Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Survival Analysis Project

914 views

Published on

  • Be the first to comment

Survival Analysis Project

  1. 1. German Breast Cancer Survival Analysis David Schuler, Ankur Verma, Udyot Kumar, Uma Lalitha-Chockalingham
  2. 2. Objectives ● Understand the length of time between breast cancer diagnoses and specific events ● Understand what factors play a role in determining these lengths
  3. 3. About Survival Analysis ● Predicting the time until an event of interest occurs ● Applications in Medicine, Manufacturing, Sociology, Sports, and many more ● Right Censored Data – an observation where the event has not yet occurred ● Survival Function - probability that at a given time, t, an event of interest has not yet occurred
  4. 4. Kaplan-Meier Estimator ● Non-parametric estimator of the survival function ● Time on the X-axis ● Percentage surviving on Y axis ● Tick marks represent right-censored observations
  5. 5. Cox Proportional Hazard Regression ● Used to look at the relationship between the survival of a patient and various explanatory variables ● Each explanatory variable is given a coefficient ○ HR = 1 : No effect ○ HR < 1 : Reduction in hazard ( Death) ○ HR > 1 : Increase in Hazard ( Death)
  6. 6. German Breast Cancer Data ● Retrieved from UMass Amherst’s Statistics website ● Data collected from clinical trials performed by the German Breast Cancer Study Group ● Total of 686 observations conducted between July 1984 and December 1989 ● 16 variables, including censoring and time-length fields for death and cancer recurrence
  7. 7. Exploratory Data Analysis
  8. 8. Correlation ● menopause and age ● Estrogen and Progesterone
  9. 9. Preliminary Survival Analysis - KM Curves
  10. 10. Preliminary Survival Analysis - KM Curves
  11. 11. Probability density function f(t) Survival function S(t) = P(T>=t) Hazard function h(t) = f(t) / S(t) A way to compare two hazard functions: Hazard ratio : HR(t) = h0 (t) / h1(t) Proportional hazard assumption : The hazard ratio does not vary with time, i.e. HR(t) = HR
  12. 12. Preliminary Survival Analysis - Cox PH ○ HR = 1 : No effect ○ HR < 1 : Reduction in hazard ( Death) ○ HR > 1 : Increase in Hazard ( Death) ● Age1 = [21,30] ● Age2 = (30,50] ● Age3 =(50,80]
  13. 13. COX Regression Modelling with phreg in SAS
  14. 14. Survival Curve Estimate ( Test Data - 3 rows)
  15. 15. Comparing R, Python & SAS Code
  16. 16. Comparing R, Python, & SAS: Plots
  17. 17. SAS Plot
  18. 18. Comparing Regression Models: Tumor Grade
  19. 19. Comparing Regression Models: Hormone
  20. 20. Comparing Regression Models: Menopause
  21. 21. References ● http://www.medicine.ox.ac.uk/bandolier/painres/download/whatis/cox_mo del.pdf ● https://media.readthedocs.org/pdf/lifelines/latest/lifelines.pdf ● https://www.cscu.cornell.edu/news/statnews/stnews78.pdf

×